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In this series of blogposts, on understanding aiki from a bio-mechanical perspective, I have made reference to key aspects of angular momentum and the behaviors of chains -- particularly the bones considered as a chain of linked rods:

While a popular and instructive video, the author's conservation of momentum theory proposed as an explanation is wrong. The correct explanation is an understanding of the effect of DYNAMIC rigidity that occurs when a chain of rods is lifted by a continuous rotation:

Quote:

[T]he chain is more like a series of short, rigid 'rods', say the authors, who publish their results today in Proceedings of the Royal Society A1. In their model, each rod is made up of three beads and two connectors. The size of a rod corresponds to the number of beads it takes to turn a section of chain back on itself by 180 degrees (it takes six).

Picking up a portion of rod from the pot with an upward force on one of its ends causes two things to happen, says Biggins. It makes the rod lift, but it also causes it to rotate. The end that is not picked up pushes downwards, and the pot provides a reaction force, he says. "The far end of the rod under those two motions actually goes down, and therefore pushes down. And that gives rise to this extra kick from the pot which drives the fountain.

(With due apologies on the title to Angus Young and Jerry Lee Lewis, respectively)

I am a firm believer in the Eastern approach of encapsulating complex observations into concrete images. But i also value the Western approach of analysis of concrete observations to find generalized principles of behavior. I believe they work far better in concert than does either one alone. Too few try to draw out the connections more rigorously and imaginatively. Both are required, I find.

This discussion, with props to Mr. Campbell, below, flows from this diagram I prepared and now christen as

Big Balls O' Aiki Water & Fire:

I have for some time used (here) a typical mechanics textbook illustration of torsional shear, shown on a cylinder, with those right-angle spirals of opposite stress. Then I realized that the issue of discontinuities in the body, their creation and resolution, controlled a great deal of the concerns on this issue. Then I recalled the "spherical" language used by both M. Ueshiba and K. Ueshiba. I also recalled that M. Ueshiba used the images of fire (upward flow or extension ) and water (downward flow or compression). So, I drew my own spherical model of the same stresses to see what it might reveal. It has revealed a more coherent dynamic that I did not suspect before I thought about this model.

[Credit to Ron Ragusa and Raul Rodrigo for inspiring me to think through this dialogue]

Q: Is Ki just mystical crap? Is it a physical, tangible thing, or just some woo-woo energy of the cosmos?

A: There are very good reasons to accept Ki as a physcial concept and a real perceptible thing that can be understood in purely physical terms, and yes, to actually justify, in a sense, some of the statements that is like an "energy" that pervades the universe.

Q: Accepting an assertion that Ki is a part of the energy spectrum pervading all the universe -- raises a few questions.

A: I'm going to take up the issue because the premise of the likely questions (and the implied belief of others on the woo-woo front) both illustrate the misperceptions of the concept of Ki, understood physically.

Q: Where in the spectrum does the energy of Ki lie?

A: Ki is the oscillation forming every wavelength of the spectrum.

Q: What is the wave length of Ki?

A: Any of them, because Ki is the wave oscillation, itself.

Q: What is the exchange particle responsible for the transmission of Ki energy?

A: Every wave/particle possesses Ki which is its oscillation. Even the background vacuum oscillates from zero to +1/-1, constantly.

Q: What theory of physics predicts the existence of Ki energy or the Ki particle?

A: All three -- classical, relativistic and quantum mechanics, are predictive of angular momentum (which defines oscillation) as a more fundamental quantity relating what we commonly distinguish as mass and energy.

The torsion tube can apply to the torso but also to the limbs and to the limbs and torso considered in a continuum.

The double pendulum can be considered as the legs from hips to ground plus the torso from hips to head. Each limb may also be separately a double pendulum, or all of them together form a chain of dependent pendula.

At first glance, these models would seem very different, a torsion tube quite static, the double pendulum quite dynamic, but the structure and dynamic of these models are, in fact, closely related.

The effect of the torque creates shear on the radial and longitudinal axis of the tube. The diagonal figure shows the resulting linear stresses of the shear -- tension in one diagonal and compression on the other. If you extend these diagonal lines around the surface of the tube, (and torsional shear is always greatest at the surface) then you get two interlaced spirals around the body of the tube.

One spiral is in compression and the other spiral is in tension. The two lines of stress are oriented 90 degrees from one another, and they are both 45 degrees off the longitudinal axis of the tube.

"Wait!" you say, "What about the double pendulum?" Well, since you askedů

Ki is rattling a bag of chicken bones in the eyes of some. I have a view of Ki, as a physical cyclic phenomenon that has a demonstrable physical basis -- and it really does rattle a bag of bones, but no chicken is involved -- unless you're just into that kind of thing -- not that there's anything wrong with that.

In response to a question about impulse of a strike it struck me (pun intended) that it is a matter not just of length of time, but of timing (in the sense of rhythm) in the frequency of the strike at impact. It matters -- not merely speed, but the actual frequency of the impact/react timing.

It requires some teensy background on force, momentum and Newton's Third Law (action= reaction).

The commonly understood linear equation F = ma can be rewritten as Σ F= dp/dt where the sum of forces is the change of momentum (p) with respect to time (t). Impulse, J = F * dt = dt* F = dt*dp/dt = dp, which is simply the change in momentum.

Very, very rarely can real world forces be treated as purely linear. Most forces are usually:
1) not isolated (there are other forces in play, with different 3D vectors),
2) dynamic, and the amount of force is changing rapidly with respect to time, and
3) eccentric (off center) as to both or all objects involved, thus involving moments (potential rotations) or actual rotations (angular momentum).

When an object is struck what strikes back (3rd law) is its moment of inertia -- its inherent reaction to havi
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Witnessing the best martial arts has an air of effortless inevitability in the outcome. It is a perception at odds with our more common perception of power, as dominating force. However dangerous or deadly, it is not the sense of imposed force that we really perceive in a profoundly capable warrior. An almost careless grace is more the image of superb martial power.

This perception remains even for those witnesses of such a performance who know better -- that slavish work that went into producing that bit of physical grace. Grace may be the best word to illustrate the contrast: power vice grace. Or grace as a foundation of a different kind of power.

The first observation about the desire for power is that is confesses a defect, a lack of something. If one were truly whole -- it should not be missing. The desire to supply the lack would not exist. Many come to the martial arts because they desire power to supply that lack, of whatever type it may be -- and there are many different types of personal sense of this deficit.

Aikido also follows this rule; however it also seems a bit different in this regard. What distinguishes many, if not most, aikidoka is that the power they tend to seek is not an increase of power over others so much as a greater power over themselves. That is the motto of the art, after all "True Victory; Self Victory; O Day of Swift Victory!"

A second observation about power: the common conception of power
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In an Aikido Journal article about Terry Dobson, http://www.aikidojournal.com/?id=3936, he related his one and only question to O Sensei in his ten years of training with him -- to please explain circle, triangle, square. O Sensei's considered response was: "Find out for yourself."

I have gone with that -- looking for an objective reality and not merely a symbolic or spiritual description behind that traditional geometric composite image. What I have gotten to, so far, fits the both the traditional description, a more rigorous physical definition as well as richly connecting to the shape and feel of the dynamics I experience in practice.

This blog entry, on topics I have been mulling over for some time now, was prompted by a discussion that was tending to elevate subjective "feel" over objective understanding of physical action. The analogy initially used was in driving, and the upshot was that driving did not require one to design or alter the basic configuration of the car. I like flying as a better analogy. It melds into one thing what the driving analogy broke into two parts-- flying involves both altering physical configuration of the vehicle of the skill as well as the skill of employing it in any given configuration. In the case of aikido, the vehicle or tool of the skill is the body (or bodies) involved. In training we gain skill in use but we also alter the way the tool functions by that use .

In a number of discussions, I have addressed the issue of angular momentum and the nature of its use according to aiki principles. This entry will sum up some of those thoughts.

I have observed that a mechanical model for the relaxed human structure is that of a linked chain of bones. This has very significant impact in the use, magnification and dissipation of forces in encounters involving aikido. The tip of a folded chain, if allowed to fall freely from the support, accelerates with nothing bu the force of gravity. And yet, the chain tip actually accelerates faster than a ball dropped simultaneously from the same height.

The reason this occurs is because of conservation of angular momentum in the free end of the chain and the addition of each increment of momentum from the successive links to those still falling as they are each brought to a halt by the tension against the support. In the limit the speed of the falling chain would go to inifitnyt but limited by the material and its dimension, it merely becomes very, very fast until it suddenly goes to zero, and rebounds against the support.

The whip operates on the same principle: a coil or loop (technically, a spiral wave) of the whip constantly decreasing in radius -- thus increasing in angular velocity by the inverse square of the radius, The kinetic energy embodied in that progression increases as the square of the velocity. The tip of the whip at full extension exceeds the sound barrier, which for
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O Sensei spent a great deal of his time in early and later life not in the dojo -- but on his farm. George Ledyard Sensei has attributed this to a desire to be more connected to nature as part of O Sensei's overall spiritual journey. http://www.aikiweb.com/columns/gledyard/2004_06.html

I think that this overlooks a less mystical and far more practical contribution of farming to the development of kokyu power as a physical sensibility. My critique is not a fault lying in the training or curriculum of any lineage, but is a systemic condition of the cirsumstance in which they find themselves teaching. The critique is common to all aikido training -- in Japan Europe or the United States, i.e.-- wherever aikido is typically practiced -- which is in cities. Almost none of their students do agricultural labor, and very few do any significant routine physical labor at all.

This may seem trivial so to some of you. I assure you it is not. Saotome Shihan and Ikeda Shihan both find a strong commonality in Ushiro Sensei's Okinawan karate budo with that of Aikido. The only direct connection between Kenji Ushiro Sensei -- a master of Okinawan karate -- and O Sensei is in fact the common element of farming. Okinawan arts are famously derived from the tools and movements common to the farmers of Okinawa, who were were prohibited from possessing ordinary weapons.

If I am correct, then this, in itself, explains the complaint by so many that the "basic" or kokyu skills of bod
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[This Blog is about technical intricacies and exploring non-aiki analogues of aiki principles, and other observations that may shed light on Aiki priciples and WHY they work the way they do. While the facts related are sound as far as they go, the application of everything here is speculative and subject verification in actual aikido practice. Choose wisely, therefore, and ask your own teacher. ]

Two dimensional state vectors at perpendicular angles (or any angle, really, but we are talking about juji + ) have a resultant that is the vector sum of the two i.e. -- a vector headed north and a vector headed west sum as a vector headed northwest. The magnitude of the vector is likewise a Pythagorean function (in the case of right angles (or a trigonometric function of the vector addition of any other angles).

But the human body is not a two dimensional object. The body as a whole can rotate in three axes about its center. Most human joints have more than one degree of freedom, some have two or three, even if some axes are more restricted, and one is a universal joint within its limits of rotation.

Dynamics of rotating objects require gyrodynamic analysis. Apply force to a rotating object and the resultant vector is ninety degrees out, on an axis that is not in the plane formed by the vector force and the axis of rotation of the object to which it is applied. This is counter-intuitive to the two-dimensional force assumptions that frame most people's walking-around knowledge, and counterintuitive to innate learning of most people's bodies. Gyrodynamic action also exists in vibrating as well rotating bodies.

To which the engineer says, most reasonably, that none of the joints in question rotate at a rate with sufficient momentum for classical gyrodynamic action. But what engineers puzzle over -- helo pilots live and die by and thus learn intuitively, wherefore
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